Study of mental disorders has entered into an exciting new era where biological measures from multiple platforms such as neuroimaging and genetics are being collected to help deepen the understanding of the disorders and improve diagnosis and treatment. Multi-dimensional data are becoming more common and hold great promise for advancing mental health research. However, effective statistical methods for extracting useful and complementary information from multi-dimensional data are still in their infancy. One of the major challenges is that multi-dimensional data often have different scales (continuous/discrete), data representations (scalar/array/matrix) and dimensions. Current analytical approaches typically conduct separate analysis within each dimension or apply simple correlative analyses. These methods are of very limited nature for uncovering latent patterns and associations in these data. This project seeks to develop novel statistical independent component analysis (ICA) methods to provide effective tools for reducing dimension, denoising and extracting features from large- scale multi-dimensional data. Specifically, the proposed methods would 1) provide a unified framework for decomposing and integrating multimodal neuroimaging data such as fMRI and DTI, 2) provide a discrete ICA model for extracting latent signals from large-scale discrete outcomes such as single-nucleotide polymorphism (SNP) genotype data, and 3) provide a joint ICA model for simultaneously decomposing neuroimaging and SNP genotype data to extract integrated imaging genetics features. The proposed statistical methods will be applied to a major depressive disorder (MDD) study, and user-friendly software will be developed and made available to general research communities. Our proposed method developments will directly benefit mental health research by providing innovative statistical tools to combine information from multi-dimensional datasets that can facilitate diagnosis, deepen mechanistic understanding and improve treatment of mental disorders. Our methods are also ubiquitous enough to be generally useful to statistical practice.